codeforces290E

奇偶建图加输出路径

#include <map>
#include <set>
#include <stack>
#include <queue>
#include <cmath>
#include <ctime>
#include <vector>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 0x3f3f3f3f
#define inf -0x3f3f3f3f
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define mem0(a) memset(a,0,sizeof(a))
#define mem1(a) memset(a,-1,sizeof(a))
#define mem(a, b) memset(a, b, sizeof(a))
typedef long long ll;
int prime[20101];
const int maxn=2001;
int a[maxn];
int Vis[maxn];
struct node{
    int x;
    int id;
}odd[maxn],even[maxn];
vector<int>ans[maxn];
struct Edge{
    int from,to,cap,flow;
    Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){}
};

struct Dinic{
    int n,m,s,t;                        //结点数,边数（包括反相弧），源点编号和汇点编号
    vector<Edge>edges;                  //边表，edges[e]和edges[e^1]互为反相弧
    vector<int>G[maxn];                 //邻接表，G[i][j]表示结点i的第j条边在e数组中的序号
    bool vis[maxn];                     //BFS使用
    int d[maxn];                        //从起点到i的距离
    int cur[maxn];                      //当前弧下标
    void AddEdge(int from,int to,int cap){
        edges.push_back(Edge(from,to,cap,0));
        edges.push_back(Edge(to,from,0,0));
        m=edges.size();
        G[from].push_back(m-2);
        G[to].push_back(m-1);
    }

    void init(int n){
        this->n=n;
        for(int i=0;i<=n;i++)
            G[i].clear();
        edges.clear();
    }

    bool BFS(){
        mem0(vis);
        queue<int>Q;
        Q.push(s);
        d[s]=0;
        vis[s]=1;
        while(!Q.empty()){
            int x=Q.front();
            Q.pop();
            for(int i=0;i<G[x].size();i++){                 //只考虑残量网络中的弧
                Edge& e=edges[G[x][i]];
                if(!vis[e.to]&&e.cap>e.flow){
                    vis[e.to]=1;
                    d[e.to]=d[x]+1;
                    Q.push(e.to);
                }
            }
        }
        return vis[t];
    }

    int DFS(int x,int a){
        if(x==t||a==0)
            return a;
        int flow=0,f;
        for(int& i=cur[x];i<G[x].size();i++){
            Edge& e=edges[G[x][i]];
            if(d[x]+1==d[e.to]&&(f=DFS(e.to,min(a,e.cap-e.flow)))>0){
                e.flow+=f;
                edges[G[x][i]^1].flow-=f;
                flow+=f;
                a-=f;
                if(a==0)
                    break;
            }
        }
        return flow;
    }

    int Maxflow(int s,int t){
        this->s=s;
        this->t=t;
        int flow=0;
        while(BFS()){
            mem0(cur);
            flow+=DFS(s,INF);
        }
        return flow;
    }

    void dfs1(int u,int top){
        Vis[u]=1;
        ans[top].push_back(u);
        //printf("%d\n",G[u].size());
        for(int i=0;i<G[u].size();i++){
            Edge& e=edges[G[u][i]];
            if(Vis[e.to]||e.to==0||e.to==n+1)
                continue;
            if(a[u]&1){
                if(e.cap-e.flow==0){
                    dfs1(e.to,top);
                }
            }
            else{
                if(e.cap-e.flow!=0){
                    dfs1(e.to,top);
                }
            }
        }
    }
};
Dinic solve;

int main(){
    int n;
    mem0(prime);
    for(int i=2;i<=20001;i++){
        if(!prime[i])
        for(int j=i*i;j<=20001;j+=i){
            prime[j]=1;
        }
    }
    /*for(int i=2;i<=100;i++){
        if(prime[i]==0)
            cout<<i<<endl;
    }*/
    while(scanf("%d",&n)!=EOF){
        solve.init(n);
        for(int i=0;i<n;i++)
            ans[i].clear();
        int cnt1=0,cnt2=0;
        for(int i=1;i<=n;i++){
            scanf("%d",&a[i]);
            if(a[i]%2==0){
                even[cnt1].x=a[i];
                even[cnt1++].id=i;
                solve.AddEdge(i,n+1,2);
            }
            else{
                odd[cnt2].x=a[i];
                odd[cnt2++].id=i;
                solve.AddEdge(0,i,2);
            }
        }
        if(n%2==1){
            printf("Impossible\n");
            continue;
        }
        for(int i=0;i<cnt2;i++)
            for(int j=0;j<cnt1;j++){
                if(prime[odd[i].x+even[j].x]==0){
                    solve.AddEdge(odd[i].id,even[j].id,1);
                }
            }
        int flow=solve.Maxflow(0,n+1);
        if(flow==n){
            mem0(Vis);
            int top=0;
            for(int i=1;i<=n;i++){
                if(Vis[i]==0){
                    solve.dfs1(i,top++);
                }
            }
            printf("%d\n",top);
            for(int i=0;i<top;i++){
                printf("%d",ans[i].size());
                for(int j=0;j<ans[i].size();j++){
                    printf(" %d",ans[i][j]);
                }
                printf("\n");
            }
        }
        else
            printf("Impossible\n");
    }
    return 0;
}